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Question

The equation of the ellipse centred at (1,2), one focus at (6,2) and passing through the point (4,6), is

A
(x1)245+(y2)220=1
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B
(x1)25+(y2)220=1
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C
(x1)220+(y2)245=1
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D
(x2)220+(y1)245=1
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Solution

The correct option is A (x1)245+(y2)220=1

Let S(6,2) and C(1,2) , slope of CS=0, therefore major axis of the ellipse is parallel to xaxis and minor axis is parallel to yaxis.
As C is the mid point of both foci
other focus S1(4,2)
We know that PS+PS1=2a
25+45=2aa2=45

Now SS1=2ae=10
a2e2=25=a2b2b2=20

Hence equation of required ellipse is
(x1)245+(y2)220=1

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